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Questions tagged [complex-systems]

This tag is for questions regarding to complex system, a system composed of many components which may interact with each other.

A complex system is a system with components that interact with each other.

Such systems are sometimes modeled as a network of nodes representing components and links representing interactions.

Examples of complex systems are Earth's climate, organisms, brains, social and economic organizations such cities, ecosystems, biological cells, and ultimately the entire universe.

Complex systems are often difficult to model due to the properties of the interactions, which include nonlinearity, emergence, spontaneous order, adaptation, and feedback loops.

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Staff icebreaker - is stasis ever attained?

Yesterday at work we had a staff day, where we were asked to play an interesting game as an icebreaker. We (50 or so people) were told to stand in a circle and choose 2 people at random out of the group. We were then asked to walk to a point so that…
martin
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Is a network a category?

in this post on math.stackexchange, the top voted answer affirmed the following quote: Roughly speaking, category theory is graph theory with additional structure to represent composition. I am wondering, are networks categories? s and if so, is…
neutrino
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Conservation of the Hamiltonian

I'm struggling with the following calculus of variation problem. For an autonomous problem, it is often said that the Hamiltonian is constant along an extremal trajectory. However, the proofs of that fact that I found in the literature rely on the…
Thomas Mariotti
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How do I perform this complex integration?

Evaluate the complex integration $(z^2 + 3z)$ wrt $z$ along the circle $|z| = 2$, from $(2,0)$ to $(0,2)$ in a counterclockwise direction. As far as I understand, this can be solved by taking $x = 2 \cos \theta$, $y = 2 \sin \theta$, and then…
Jasmine
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Do a complex system's attribute changes always exhibit depedance?

Say a complex system C has an attribute A. Can I assert that a change of A is always – to some degree – dependent upon A’s past? My reasoning is the following: Any attribute of C is influenced by C. Therefore A’s current value is always a result…
cardycakes
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Lie Algebra of Endemic SIRS Model

I'm currently working in the endemic SIRS bihamiltonian structure such that the Poisson brackets, Hamiltonian and Casimir are given by: $$H=S+I+R$$ $$\left\{ S, I\right\}= 0 \hspace{2cm} \left\{S,R\right\}=-\beta SI+\mu I \hspace{2cm}…
jnava1612
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Does the inverted single pendulum have a positive Lyapunov exponent?

I'm doing some numerical experiments to test an integrator, and I got this plot, for the motion of 5 pendula, whose initial displacement differ by $10^{-6}$ radians away from straight up ($\theta_0 = \pi - d\theta$, where…
David
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Tensorial Representation of a Complex Network (Questions on Tensors)

INTRODUCTION TO QUESTION 1 Some authors proposed a tensorial representation of complex networks (for both single layer networks and multilayer networks). One reference paper for this topic is this one: M. De Domenico et al., Mathematical…
Ommo
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How much algebra is preferable for studying/doing research in dynamical/complex system and networks

This question seems quite broad to ask... The situation here is that I'm a second-year undergrad student majoring in math and statistics. I'm really interested in fields like complex system and dynamics on/of networks and would like to plan for…
J-A-S
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Strange fixed point in state space

I'm studying the following dynamical system, \begin{align} \dot{x} &= y \,\, , \\ \dot{y} &= \frac{\left(-4 x^3+33 x^2-78 x+54\right) y^2+(x-3) (2 x-6)^2}{(3-2 x) (2-x) x (2 x-6)} \,\, , \end{align} and when I plot the phase space I get the…
Herr Schrödinger
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Stability of delay differential equations

I have encountered a 2-dimensional system of differential equations. One of them is a delay differential equation (DDE). Can anybody explain to me how to analyze the stability of a DDE?
Bárbara Mota
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Expanding growth rate (linear stability analysis)

I have done a linear stability analysis for a system of coupled PDEs. The growth rate of perturbations, $\lambda$, satisfies an equation $f(\lambda)=0$. Now I want to find the leading order terms in the growth rate. I did two methods to find the…
questionerno8
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How do you explain (in writing) a complicated mathematical object in a general sense whilst avoiding ambiguity?

I'm writing research that involves explaining objects which are fairly complicated and very specific to the research in question (e.g. a new type of mathematical model of something). The objects in question may have complicated constraints or…
Jonathan
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Trying to understand Ligthill-Whitham traffic model

I am reading this paper, describing an ODE-based traffic model. Initially it starts with a PDE model, which is then simplified to obtain a more tractable ODE one. I'm trying to understand the initial PDE model. I am new to traffic modeling (and PDEs…
mell_o_tron
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Why do we refer to Lyapunov exponents as a characteristic of the system, telling us about its chaoticity, when it is only referred to a point?

Lyapunov exponents are defined as indicators of the sensibility to initial conditions. In fact, they give the mean rate of exponential separation of trajectories. They are, however, specific of a given point, in which the Jacobian matrix that…
Federica Sibilla
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